Many industries employ sophisticated manufacturing equipment that includes multiple sensors and controls, each of which may be carefully monitored during processing to ensure product quality. One method of monitoring the multiple sensors and controls is statistical process monitoring (a means of performing statistical analysis on sensor measurements and process control values (process variables)), which enables automatic detection and/or diagnosis of “faults.” A “fault” can be a malfunction or maladjustment of manufacturing equipment (e.g., deviation of a machine's operating parameters from intended values), or an indication of a need for preventive maintenance to prevent an imminent malfunction or maladjustment. Faults can produce defects in the devices being manufactured. Accordingly, one goal of statistical process monitoring is to detect and/or diagnose faults before they produce such defects.
During process monitoring, a fault is detected when one or more of the statistics of recent process data deviate from a statistical model by an amount great enough to cause a model metric to exceed a respective confidence threshold. A model metric is a scalar number whose value represents a magnitude of deviation between the statistical characteristics of process data collected during actual process monitoring and the statistical characteristics predicted by the model. Each model metric is a unique mathematical method of estimating this deviation. Conventional model metrics include Squared Prediction Error (commonly referred to as SPE, Qres, or Q), and Hotelling's T2 (T2).
Each model metric has a respective confidence threshold, also referred to as a confidence limit or control limit, whose value represents an acceptable upper limit of the model metric. If a model metric exceeds its respective confidence threshold during process monitoring, it can be inferred that the process data has aberrant statistics because of a fault.
An obstacle to accurate fault detection is the fact that manufacturing processes commonly drift over time, even in the absence of any problems. For example, the operating conditions within a semiconductor process chamber typically drift between successive cleanings of the chamber and between successive replacements of consumable chamber components. Conventional statistical process monitoring methods for fault detection suffer shortcomings in distinguishing normal drift from a fault.
Specifically, some fault detection methods employ a static model, which assumes that process conditions remain constant over the life of a tool. Such a model does not distinguish between expected changes over time and unexpected deviations caused by a fault. To prevent process drift from triggering numerous false alarms, the control limit must be set wide enough to accommodate drift. Consequently, the model may fail to detect subtle faults.
Gallagher, Neal B. et al., “Development and benchmarking of multivariate statistical process control tools for a semiconductor etch process: improving robustness through model updating”, ADCHEM 1997, Banff, Canada; and Li, Weihua et al., “Recursive PCA for adaptive process monitoring”, J. Process Control, vol. 10, pp. 471-486 (2000) each describe methods of responding to drifts in the process conditions by periodically adapting a model to drifts in process data. The Gallagher publication describes adaptation of mean and covariance statistics. Gallagher attempts to distinguish between faults and normal drifts by identifying an occurrence of a fault if either a Q or T2 metric for a model exceeds a confidence limit. The Li publication describes adaptation of mean, covariance, principal component matrix, and number of principal components in a principal component analysis (PCA) model. Neither of the methods of adapting as suggested by Gallagher and Li detects faults that occur gradually.
Spitzlsperger, Gerhard et al., “Fault detection for a via etch process using adaptive multivariate methods”, ISSM, Tokyo, Japan (2004) discloses the use of human expert knowledge to adapt only univariate mean and scaling coefficients that are expected to drift. However, by adapting only univariate means and scaling coefficients, this method fails to provide adaptation of the covariances between variables within a model.
Each of the conventional adaptation methods described above is susceptible to cumulative computational rounding errors, which are caused by the periodic adaptations. This results in the models having inaccurate statistical values that can cause both false alarms and a failure to detect actual faults.